FIG. 9 is a block diagram showing an example of a conventional target tracking device. This target tracking device comprises a passive sensor 1, a passive sensor processing unit 2, an active sensor 3, an active sensor processing unit 4, and a data fusion unit 5. The active sensor 3 and the active sensor processing unit 4 are external devices.
The passive sensor 1 measures the angle of a radio wave, infrared rays, a sound wave, or the like radiated (and reradiated) from a target. That is, the passive sensor 1 measures the angle of the target, thereby obtaining passive measurement of the target angle (i.e. goniometric data; hereinafter it is called as passive measurement). The passive sensor 1 sends the passive measurement to the passive sensor processing unit 2.
The passive sensor processing unit 2 calculates a predicted state and an updated state (i.e. a smoothed state) based on the passive measurement from the passive sensor 1. The passive sensor processing unit 2 sends the predicted state and the updated state to the data fusion unit 5 as the target track. Based on the target track, the passive sensor processing unit 2 generates a control signal to control the posture and the like of the passive sensor 1, and sends the signal to the passive sensor 1.
The active sensor 3 radiates an electromagnetic wave or a sound wave. The active sensor 3 measures the distance and angle of the electromagnetic wave or sound wave reflected by the target. That is, the active sensor 3 measures the distance and angle of the target, thereby obtaining active measurement of the target distance and angle (hereinafter it is called as active measurement). The active sensor 3 sends the active measurement to the active sensor processing unit 4.
Like the passive sensor processing unit 2, the active sensor processing unit 4 calculates a predicted state and an updated state based on the active measurement from the active sensor 3. The active sensor processing unit 4 sends the predicted state and the updated state to the data fusion unit 5 as the target track. Based on the target track, the active sensor processing unit 4 generates a control signal to control the posture and the like of the active sensor 3, and sends the signal to the active sensor 3.
The data fusion unit 5 determines whether the target track from the passive sensor processing unit 2 and that from the active sensor processing unit 4 correspond to the same target. Upon determining that the target tracks correspond to the same target, the data fusion unit 5 combines these target tracks. A thus obtained combined track is externally output.
FIG. 10A is a flowchart showing an exemplary processing procedure of the passive sensor processing unit 2 shown in FIG. 9. FIG. 10B is a flowchart showing an exemplary processing procedure of the data fusion unit 5 shown in FIG. 9.
Referring to FIG. 10A, when processing starts, a measurement data is input to the passive sensor processing unit 2 (ST101). That is, the passive sensor 1 measures the target based on the control signal from the passive sensor processing unit 2, and sends the passive measurement of the target obtained by the measurement to the passive sensor processing unit 2. The passive sensor processing unit 2 acquires the passive measurement sent from the passive sensor 1.
Prediction processing is executed (ST102). That is, the passive sensor processing unit 2 calculates the predicted state of the target and its covariance matrix based on the updated state of the target and its covariance matrix calculated in step ST103 of the preceding measurement.
Update processing is then executed (ST103). That is, based on the passive measurement from the passive sensor 1 and the predicted state of the target and its covariance matrix calculated in step ST102, the passive sensor processing unit 2 calculates the updated state of the target and its covariance matrix and outputs them as the target track.
Control processing is executed (ST104). That is, based on the target track, the passive sensor processing unit 2 generates a control signal to control the posture and the like of the passive sensor 1, and sends the signal to the passive sensor 1. The processing of steps ST101 to ST105 is continued until the end.
Referring to FIG. 10B, when processing starts, track is input to the data fusion unit 5 (ST201). That is, the target track from the passive sensor processing unit 2 and the target track from the active sensor processing unit 4 are input to the data fusion unit 5.
Data fusion processing is executed (ST202). That is, the data fusion unit 5 combines the target track from the passive sensor processing unit 2 and the target track from the active sensor processing unit 4. The obtained combined track is externally output. Details of the data fusion processing will be described later. The processing of steps ST201 to ST203 is continued until the end.
The processing contents of the passive sensor processing unit 2 will be described in detail. The motion model of the target is defined in the following way. Note that “bar x” will be expressed as “x(−)” hereinafter.
                                          x            _                                k            +            1                          =                                            F                              k                +                1                                      ⁢                                          x                _                            k                                +                                    G                              k                +                1                                      ⁢                          w              k                                                          (        1        )                                                      x            _                    k                =                  [                                                                      a                  k                                                                              e                  k                                                                                                  a                    .                                    k                                                                                                  e                    .                                    k                                                              ]                                    (        2        )                                          F                      k            +            1                          =                  [                                                                      I                  2                                                                                                  (                                                                  t                                                  k                          +                          1                                                                    -                                              t                        k                                                              )                                    ·                                      I                    2                                                                                                                        O                  2                                                                              I                  2                                                              ]                                    (        3        )                                          G                      k            +            1                          =                  [                                                                                                                                        (                                                                              t                                                          k                              +                              1                                                                                -                                                      t                            k                                                                          )                                            2                                        2                                    ·                                      I                    2                                                                                                                                            (                                                                  t                                                  k                          +                          1                                                                    -                                              t                        k                                                              )                                    ·                                      I                    2                                                                                ]                                    (        4        )                                          Q          k                =                              1                          r              k                                ⁡                      [                                                                                                      (                                              σ                        k                        h                                            )                                        2                                                                    0                                                                              0                                                                                            (                                              σ                        k                        v                                            )                                        2                                                                        ]                                              (        5        )            where x(−)k is a state vector including an azimuth ak, an elevation ek, and their velocity components at a measurement time tk, Fk+1 and Gk+1 are the transition matrix and the driving matrix from the measurement time tk to a measurement time tk+1, respectively, wk is the process noise vector at the measurement time tk for an average 0 and a covariance matrix Qk, σhk and σvk are the standard deviations of the horizontal and vertical planes of process noise at the measurement time tk, respectively, rk is the distance from the passive sensor 1 to the target at the measurement time tk, AT is the transposition of a vector or matrix A, In is an n×n identity matrix, and On is an n×n zero matrix.
The measurement model of the passive sensor 1 is defined by
                              y          k                =                                            H              k                        ⁢                                          x                _                            k                                +                      v            k                                              (        6        )                                          H          k                =                  [                                                    1                                            0                                            0                                            0                                                                    0                                            1                                            0                                            0                                              ]                                    (        7        )                                          R          k                =                  [                                                                                          (                                          σ                      k                      a                                        )                                    2                                                            0                                                                    0                                                                                  (                                          σ                      k                      e                                        )                                    2                                                              ]                                    (        8        )            where yk is the measurement vector of the passive sensor 1 at the measurement time tk, Hk is the measurement matrix of the passive sensor 1 at the measurement time tk, vk is the measurement noise vector of the passive sensor 1 at the measurement time tk for an average 0 and a covariance matrix Rk, and σak and σek are the standard deviations of the azimuth and elevation of measurement noise at the measurement time tk, respectively.
In step ST101, the passive measurement from the passive sensor 1 is input as the measurement vector yk.
In step ST102, prediction processing represented by the following equations is executed using the result of update processing of the preceding measurement. Note that “hat x” will be expressed as “x(^)” hereinafter.
                                          x            ^                                k            ❘                          k              -              1                                      =                              F            k                    ⁢                                    x              ^                                                      k                -                1                            ❘                              k                -                1                                                                        (        9        )                                          P                      k            ❘                          k              -              1                                      =                                            F              k                        ⁢                                                            P                                                            k                      -                      1                                        ❘                                          k                      -                      1                                                                      ⁡                                  (                                      F                    k                                    )                                            T                                +                                    G              k                        ⁢                                                            Q                                      k                    -                    1                                                  ⁡                                  (                                      G                    k                                    )                                            T                                                          (        10        )                                          Q                      k            -            1                          =                              1                          r              preset                                ⁡                      [                                                                                                      (                                              σ                                                  k                          -                          1                                                h                                            )                                        2                                                                    0                                                                              0                                                                                            (                                              σ                                                  k                          -                          1                                                v                                            )                                        2                                                                        ]                                              (        11        )            where x(^)k|k−1 and Pk|k−1 are the predicted state vector and the predicted error covariance matrix at the measurement time tk, respectively, and x(^)k−1|k−1 and Pk−1|k−1 are the updated state vector (i.e. the smoothing vector) and the updated error covariance matrix at a measurement time tk−1, respectively. Since a true value rk−1 of the target distance cannot be known, a preset target distance rpreset is used when calculating a process noise covariance matrix Qk−1.
In step ST103, update processing represented by the following equations is executed using the measurement vector from the passive sensor 1 and the result of prediction processing. Note that “tilde y” will be expressed as “y(˜)” hereinafter.{tilde over (y)}k=yk−Hk{circumflex over (x)}k|k−1  (12)Sk=HkPk|k−1(Hk)T+Rk  (13)Kk=Pk|k−1(Hk)T(Sk)−1  (14){circumflex over (x)}k|k={circumflex over (x)}k|k−1+Kk{tilde over (y)}k  (15)Pk|k=(I4−KkHk)Pk|k−1  (16)where y(˜)k is the residual vector of the passive sensor 1 at the measurement time tk, Sk is the residual covariance matrix of the passive sensor 1 at the measurement time tk, Kk is the Kalman gain matrix of the passive sensor 1 at the measurement time tk, x(^)k|k and Pk|k are the updated state vector and the updated error covariance matrix at the measurement time tk, respectively, and A−1 is the inverse matrix of the matrix A.
In step ST104, control processing is executed. In step ST105, terminate determination processing is executed. Details of data fusion processing of step ST202 will be explained next.
FIG. 11 is a flowchart illustrating details of data fusion processing in FIG. 10B. Referring to FIG. 11, when data fusion processing starts, the correlation processing is performed (ST301). That is, the data fusion unit 5 determines whether the target track from the passive sensor processing unit 2 and that from the active sensor processing unit 4 are of the same target.
Combined track calculation processing is then performed (ST302). That is, upon determining in step ST301 that the target track from the passive sensor processing unit 2 and the target track from the active sensor processing unit 4 are of the same target, the data fusion unit 5 combines the two target track. New data obtained by combining them is externally output as the combined track.
In the tracking processing of the passive sensor 1, the process noise covariance matrix Qk−1 includes an error because the distance data from the passive sensor 1 to the target is not available. It is consequently difficult to calculate the optimum value of the filter gain (Kalman gain matrix) that is indirectly calculated from the process noise covariance matrix and used to calculate the track. Hence, the track error of the target becomes large.
If the error of track calculated by the passive sensor processing unit 2 is large, the track error of the combined track calculated by the data fusion unit 5 is also large. This is because the combined track is calculated based on the target track from the passive sensor processing unit 2 and that from the active sensor processing unit 4.
Even for a target that performs constant velocity (non-maneuver) on the orthogonal coordinate system, an angular acceleration and the differential component of the angular acceleration are generated on the polar coordinate system. Since it is difficult to estimate the component from target angle and reflect it on the process noise covariance matrix Qk−1, the track error becomes large.
As a technique of improving the tracking performance for both a target that performs non-maneuver and a target that performs maneuver, an Interacting Multiple Model (IMM) filter is known, which operates a plurality of motion models in parallel. The IMM filter is applicable to the processing of the active sensor processing unit 4. However, since many motion models are generally defined as a motion on a three-dimensional orthogonal coordinate system, it is difficult to apply the technique to the passive sensor processing unit 2 that estimates the target track on a two-dimensional polar coordinate system or the like.
As described above, in the target tracking device using a passive sensor, the distance data from the passive sensor 1 to the target is not obtained in general. It is therefore difficult to calculate the optimum value of the filter gain to be used to calculate the track, and the track error becomes large.
Since the distance data to the target cannot be obtained, the target is tracked on a local coordinate system about the passive sensor. However, when, for example, a polar coordinate system is used as the local coordinate system, an angular acceleration and the differential component of the angular acceleration are generated on the polar coordinate system even if the target performs constant velocity (non-maneuver) on the orthogonal coordinate system.
When the filter gain is increased to cope with the above-described problem, the random component of the track error becomes large. When the filter gain is decreased to make the random component of the track error smaller, the bias component of the track error becomes large. At any rate, it is difficult to improve the tracking performance. Even performing data fusion using track calculated by the passive sensor processing unit does not allow to improve the accuracy of the combined track. That is, the target tracking device using both the passive sensor and the active sensor needs to reduce the error caused by the passive sensor because it affects the total performance.
When a technique assuming a single motion model is optimized for a target that performs non-maneuver, tracking performance for a target that performs maneuver degrades. Similarly, when the technique is optimized for a target that performs maneuver, tracking performance for a target that performs non-maneuver degrades. That is, it is difficult for the existing technique to improve the tracking performance for both a target that performs non-maneuver and a target that performs maneuver.